[new feature] Auto-deploy preview server with a workflow_dispatch action

Now that #2153 is merged we're well on our way to have a preview server where we can test features in close-to-prod conditions.

The current solution is not ideal however, because a lot of it is still quite manual. Things should ideally be more automated.

One idea [raised in the comments](https://github.com/django/djangoproject.com/pull/2153#issuecomment-3170677967) of the "preview branch" PR was to switch to a `workflow_dispatch` github action and combine that with some form of automatic deployment. I think that's a good idea.

The way I understand there are two parts to this feature:

- [ ] Replacing the current `preview` branch tagging github action (see #2153) with a manually triggered `workflow_dispatch`. This could be done by any contributor
- [ ] Setting up an automatic deployment on the preview server. This will need to be done by someone from the ops team (likely me), but the technical approach could be discussed in this ticket

Start by inspecting the current `preview` branch tagging GitHub Action described in #2153 and the workflow-dispatch idea in the linked comment. Done means replacing the tagging action with a manually triggered workflow and agreeing on an automatic preview-server deployment approach with the ops team.

Written by the indexing model from the issue text.